LeetCode 2447: Number of Subarrays With GCD Equal to K Solution

Master LeetCode problem 2447 (Number of Subarrays With GCD Equal to K), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2447. Number of Subarrays With GCD Equal to K

Medium

Array Math Number Theory

Problem Explanation

Explanation:

To solve this problem, we can iterate through all subarrays of the given array nums and calculate the greatest common divisor (GCD) of each subarray. If the GCD of a subarray is equal to the given value k, we increment the count of valid subarrays. We can calculate the GCD of a subarray efficiently using Euclidean algorithm. The time complexity of this approach is O(n^2 * log(max(nums))) where n is the length of the array nums and max(nums) is the maximum value in the array. The space complexity is O(1).

Solution Code

class Solution {
    public int countSubarraysWithGCD(int[] nums, int k) {
        int count = 0;
        for (int i = 0; i < nums.length; i++) {
            int curGcd = 0;
            for (int j = i; j < nums.length; j++) {
                curGcd = gcd(curGcd, nums[j]);
                if (curGcd == k) {
                    count++;
                }
            }
        }
        return count;
    }

    private int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
}

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